Random vectors with HNBUE-type marginal distributions
The paper focuses on the preservation problem for nonparametric life distribution classes under addition of life lengths. The author investigates one of the largest of these life distribution classes, namely the class of Harmonic New Better than Used in Expectation (HNBUE). The main result of this note is to prove, using a stochastic order representation of HNBUE distributions, that the closure under addition property for the HNBUE class continues to hold even when removing the assumption of independence among summands. A consequence of this result is that the distribution of a random vector with HNBUE marginal distributions is uniquely determined by its mixed moments of positive order. Another derived result is that the family of random vectors with HNBUE marginal distributions is closed under convergence in law, and that convergence in law is equivalent to convergence of moments. An application of these results to portfolio choice theory shows that any diversified portfolio of non-independent prospects is preferred to specialized portfolios by every risk averter individual.
scientific article; zbMATH DE number 1546531
scientific article